Combinatorial Nullstellensatz over division rings

Elad Paran

doi:10.1007/s10801-023-01263-1

Combinatorial Nullstellensatz over division rings

Elad Paran

Mathematics discipline

Research output: Contribution to journal › Article › peer-review

Abstract

We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.

Original language	English
Pages (from-to)	895-911
Number of pages	17
Journal	Journal of Algebraic Combinatorics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s10801-023-01263-1
State	Published - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Combinatorial Nullstellensatz
Division rings
Noncommutative ring theory

Access to Document

10.1007/s10801-023-01263-1

Cite this

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abstract = "We extend Alon{\textquoteright}s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.",

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AB - We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.

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KW - Noncommutative ring theory

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Combinatorial Nullstellensatz over division rings

Abstract

Bibliographical note

Keywords

Access to Document

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